The mystery of sticking egg shell was still unsolved. I was still thinking about it so I continued doing experiment.
I was thinking if the phenomenon was similar to fish sticking to pan during frying. The egg is mostly protein, just like fish. Protein sticks to metal surface when heated slowly. High heat is needed to curd the protein fast and prevent it from sticking.
There will be no harm if I try so I bought another two eggs and boiled over a very low heat. Boiling commenced after 15 minutes. Then I let it boiled for another 15 minutes. A total of 30 minutes cooking time. I opened the egg and still got the same silky smooth egg. My wild guess was still wrong.
My knowledge was not enough. I needed some digging to find it out. It is stated on Yahoo answers that fresh eggs are hard to peel when boiled. Older eggs about two days old and over loosen the stickiness and become relatively easy to peel.
So the egg with sticking shell is a sign of freshness. The sticking egg shell should not be annoying. If you have not experienced sticking eggshell yet, then you have not eaten a fresh one.
Edinformatics.com has a detailed explanation for this. Fresh eggs have acidic environment causing the albumen to stick to inner shell membrane- the plastic like lining. As the egg gets older the shell protective coating is washed off which permits air entry. It reduce the acidity and loosen the albumen.
I gonna continue this when a fresh egg is available.